Question: A circle with circumference ${12}$ has an arc with a $48^\circ$ central angle. What is the length of the arc?
The ratio between the arc's central angle ${\theta}$ and $360^\circ$ is equal to the ratio between the arc length ${s}$ and the circle's circumference ${c}$. $\dfrac{{\theta}}{360^\circ} = \dfrac{{s}}{{c}}$ $\dfrac{{48}^\circ}{360^\circ} = \dfrac{{s}}{{{12}}}$ $\dfrac{2}{15} = \dfrac{{s}}{{12}}$ $\dfrac{2}{15} \times {12} = {s}$ $\dfrac{8}{5} = {s}$ ${12}$ ${48^\circ}$ ${\dfrac{8}{5}}$